{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b70e20aa-7975-418c-9677-3d5a4b5dcd93",
   "metadata": {},
   "source": [
    "Chapter 04\n",
    "\n",
    "# 3 x 3方阵行列式对应平行六面体体积\n",
    "《线性代数》 | 鸢尾花书：数学不难"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac6e6fda-2afa-44bc-98f3-df0b0efb8df9",
   "metadata": {},
   "source": [
    "这段代码从数学的角度，旨在构造并可视化一个由三维空间中三个向量张成的**平行六面体（Parallelepiped）**。具体过程涉及线性代数中向量、矩阵、向量加法和几何可视化的核心概念。\n",
    "\n",
    "---\n",
    "\n",
    "### 一、向量空间与矩阵列向量\n",
    "\n",
    "首先，定义了一个 $3 \\times 3$ 的实矩阵：\n",
    "$$\n",
    "A = \\begin{bmatrix}\n",
    "2 & 0 & 2 \\\\\n",
    "2 & 2 & 0 \\\\\n",
    "0 & 2 & 2\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "矩阵 $A$ 的每一列向量分别定义为：\n",
    "- $ \\mathbf{a}_1 = A[:, 0] = \\begin{bmatrix} 2 \\\\ 2 \\\\ 0 \\end{bmatrix} $\n",
    "- $ \\mathbf{a}_2 = A[:, 1] = \\begin{bmatrix} 0 \\\\ 2 \\\\ 2 \\end{bmatrix} $\n",
    "- $ \\mathbf{a}_3 = A[:, 2] = \\begin{bmatrix} 2 \\\\ 0 \\\\ 2 \\end{bmatrix} $\n",
    "\n",
    "这三个向量 $\\mathbf{a}_1, \\mathbf{a}_2, \\mathbf{a}_3$ 构成了三维欧几里得空间 $\\mathbb{R}^3$ 中的一个向量组，它们线性无关，因此可以张成一个三维体积 —— 即平行六面体。\n",
    "\n",
    "---\n",
    "\n",
    "### 二、平行六面体的几何构造\n",
    "\n",
    "平行六面体是由原点 $O = (0, 0, 0)$ 及上述三个向量经过向量加法构造出的八个顶点：\n",
    "\n",
    "- $P_1 = \\mathbf{a}_1$\n",
    "- $P_2 = \\mathbf{a}_2$\n",
    "- $P_3 = \\mathbf{a}_3$\n",
    "- $P_4 = \\mathbf{a}_1 + \\mathbf{a}_2$\n",
    "- $P_5 = \\mathbf{a}_1 + \\mathbf{a}_3$\n",
    "- $P_6 = \\mathbf{a}_2 + \\mathbf{a}_3$\n",
    "- $P_7 = \\mathbf{a}_1 + \\mathbf{a}_2 + \\mathbf{a}_3$\n",
    "\n",
    "这 8 个顶点构成了平行六面体的结构，其六个面由 4 个顶点构成的平行四边形组成，具体如下：\n",
    "\n",
    "- 底面：$[O, P_1, P_4, P_2]$\n",
    "- 前侧面：$[O, P_2, P_6, P_3]$\n",
    "- 右侧面：$[O, P_1, P_5, P_3]$\n",
    "- 顶面：$[P_7, P_4, P_1, P_5]$\n",
    "- 左后侧面：$[P_7, P_4, P_2, P_6]$\n",
    "- 背面：$[P_7, P_5, P_3, P_6]$\n",
    "\n",
    "---\n",
    "\n",
    "### 三、几何解释与体积\n",
    "\n",
    "该平行六面体的体积等于这三个向量所张成的**混合积**（triple scalar product）的绝对值：\n",
    "$$\n",
    "V = |\\mathbf{a}_1 \\cdot (\\mathbf{a}_2 \\times \\mathbf{a}_3)|\n",
    "$$\n",
    "这是一个标量，反映了这三个向量张成的有向体积。\n",
    "\n",
    "---\n",
    "\n",
    "### 四、图像可视化与三维渲染\n",
    "\n",
    "代码最后使用 Matplotlib 的三维绘图工具 `mpl_toolkits.mplot3d` 来绘制：\n",
    "\n",
    "- 以原点为起点画出三根向量 $\\mathbf{a}_1$（红色）、$\\mathbf{a}_2$（绿色）、$\\mathbf{a}_3$（蓝色）\n",
    "- 构建一个透明的黄色平行六面体，用于表示这三个向量张成的空间区域\n",
    "- 设置三维坐标轴的范围与标签，使得图像清晰显示向量关系及几何体的构造\n",
    "- 使用正投影（`ax.set_proj_type('ortho')`）以及调整视角增强空间感\n",
    "\n",
    "---\n",
    "\n",
    "总结而言，这段代码将一个 $3 \\times 3$ 矩阵 $A$ 看作由三个列向量组成的向量组，并利用它们在三维空间中构造一个几何体（平行六面体），进而通过三维图形方式可视化它们的空间组合关系。这不仅展示了线性代数中“张成空间”的概念，也提供了几何直观认知。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d70f69a8-d3be-4e31-b7bb-e29165e3c577",
   "metadata": {},
   "source": [
    "## 初始化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0afc471c-288e-48e0-9c23-0377b9a126ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d.art3d import Poly3DCollection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "272cbc29-0a1b-4f3b-875e-e6de1091568d",
   "metadata": {},
   "source": [
    "## 定义一个 3×3 矩阵 A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85d23140-12d3-4177-8fdf-fde5d80e7aa6",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[2, 0, 2],\n",
    "              [2, 2, 0],\n",
    "              [0, 2, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ac678cd-df93-40e5-822d-14cf56d4fbdd",
   "metadata": {},
   "source": [
    "## 提取列向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aee41c76-bd66-4093-8b0c-c9898410f6f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "a1 = A[:, 0]\n",
    "a2 = A[:, 1]\n",
    "a3 = A[:, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6b72b5d-49c8-4caa-890a-728062e7f38d",
   "metadata": {},
   "source": [
    "## 构造平行六面体的8个顶点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17d4198c-c8b4-485d-a9dd-6e751d1107ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "O = np.array([0, 0, 0])\n",
    "P1 = a1\n",
    "P2 = a2\n",
    "P3 = a3\n",
    "P4 = a1 + a2\n",
    "P5 = a1 + a3\n",
    "P6 = a2 + a3\n",
    "P7 = a1 + a2 + a3\n",
    "\n",
    "vertices = [O, P1, P2, P4, P3, P5, P6, P7]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1adbf1d4-c09e-4ad7-818b-7ce965f73155",
   "metadata": {},
   "source": [
    "## 定义六个面"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e54c21b-a242-4c01-96f7-f6820ce6e704",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 每个面是4个点\n",
    "faces = [\n",
    "    [O, P1, P4, P2],  # 底面\n",
    "    [O, P2, P6, P3],  # 侧面\n",
    "    [O, P1, P5, P3],  # 侧面\n",
    "    [P7, P4, P1, P5], # 上面\n",
    "    [P7, P4, P2, P6], # 侧面\n",
    "    [P7, P5, P3, P6]  # 背面\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfb4b316-50a4-4051-8b9d-796290e5c5e2",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf56b58b-cded-4881-8832-88cfa8c544b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# 绘制向量箭头\n",
    "ax.quiver(0, 0, 0, *a1, color='red', linewidth=2)\n",
    "ax.quiver(0, 0, 0, *a2, color='green', linewidth=2)\n",
    "ax.quiver(0, 0, 0, *a3, color='blue', linewidth=2)\n",
    "\n",
    "# 绘制平行六面体\n",
    "face_collection = Poly3DCollection(faces, alpha=0.3, \n",
    "                                   facecolor='yellow', \n",
    "                                   edgecolor='black', ls = '--')\n",
    "ax.add_collection3d(face_collection)\n",
    "\n",
    "# 图像装饰\n",
    "ax.set_xlim([0, 3])\n",
    "ax.set_ylim([0, 3])\n",
    "ax.set_zlim([0, 3])\n",
    "ax.set_xlabel(\"x1\")\n",
    "ax.set_ylabel(\"x2\")\n",
    "ax.set_zlabel(\"x3\")\n",
    "ax.view_init(elev=30, azim=30)  # 设置视角\n",
    "ax.set_proj_type('ortho')\n",
    "ax.set_box_aspect([1,1,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3e1ddda-7c83-4668-afea-963e788dee52",
   "metadata": {},
   "source": [
    "作者\t**生姜DrGinger**  \n",
    "脚本\t**生姜DrGinger**  \n",
    "视频\t**崔崔CuiCui**  \n",
    "开源资源\t[**GitHub**](https://github.com/Visualize-ML)  \n",
    "平台\t[**油管**](https://www.youtube.com/@DrGinger_Jiang)\t\t\n",
    "\t\t[**iris小课堂**](https://space.bilibili.com/3546865719052873)\t\t\n",
    "\t\t[**生姜DrGinger**](https://space.bilibili.com/513194466)  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
   "name": "conda-base-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
